Homework Help

Solve for x: 4(3x+7)=7

user profile pic

sam-mccomb | Student, Grade 9 | eNotes Newbie

Posted June 6, 2009 at 8:00 AM via web

dislike 3 like

Solve for x:

4(3x+7)=7

18 Answers | Add Yours

user profile pic

buffy-the-vampire-slayer | Student, Undergraduate | eNotes Newbie

Posted June 6, 2009 at 8:48 AM (Answer #1)

dislike 1 like

im not sure how your teacher asked you to solve the equations, but theres simple steps to follow to figure out for x;

  1. you want to get rid of the brackets, to do this multiply the numbers in brackets by 4
  2. rewrite the question, it should now be 12x + 28 =7
  3. now you want to isolate x, to do this subtract 28 from both sides of the equation
  4. rewrite the equation once again, it should now be 12x = -21
  5. now divide both sides of the equation by 12
  6. rewrite the equation one more time and you have your answer. x= -1.75
  7. dont forget to check your answer! :)
user profile pic

kjcdb8er | Teacher | (Level 1) Associate Educator

Posted June 6, 2009 at 8:48 AM (Answer #2)

dislike 1 like

4(3x+7)=7

(3x+7)=7/4                    divide both sides by 4

3x = 7/4 - 7              subtract 7 from both sides

x = (7/4 - 7)/3         divide both sides by 3

x = 7/12 -7/3           expand the parenthesis

x = 7/12 - 28/12       find common denominator (* by 4/4)

x = -21/12               subtract

x = -7/4 simplify

user profile pic

neela | High School Teacher | Valedictorian

Posted June 6, 2009 at 11:26 AM (Answer #3)

dislike 1 like

4(3x+7)=7.

To solve for x, multiply by 4 to each of the terms inside the bracket in the left side:4*3x=12x. 4*-7=-28. The right side is retained as it is:

12x+28=7.

Subtract 28 from  both sides to retain the unknown term 12x on the left and the known term or the numbers on the right:

12x+28-28=7-28.

Now 28-28 on the left cancel out.On the right 7-28= -21:

12x=-21.

Divide both sides by 12.  On the left 12x/12 becomes x.On the right -21/12, which is reduced to -7/4 in the lowest equivalent fraction form.

Therefore, x=-7/4  .

Convert 7/4 in decimal form and attach the minus line at last.

7/4=1+3/4 =1.75.

Therefore,x=-1.75 is our solution.

 

Tally:

Put the solution, x=-1.75 in the original equation and see whether the equation is satisfied, in the sense the value on the left becomes equal to the right.

Left side :4*[3(-1.75)+7]=4*3(-1.75)+4*7=4*-5.25+28=-21+28=7.

Right side:7

Both sides are equal in value after putting x=-1.75. So the solution is verified.

 

user profile pic

Jyotsana | Student, Grade 10 | Valedictorian

Posted February 9, 2014 at 1:11 AM (Answer #10)

dislike 1 like

4(3x+7)=7

12x+28=7

12x+28-28=7-28

12x=-21

12x/12=-21/12

x=-1.75

user profile pic

fahad-alfahad | eNotes Newbie

Posted June 6, 2009 at 1:01 PM (Answer #4)

dislike 0 like

4(3x+7)=7   ======>multiply 4 by 3x , 7

12x + 28 = 7     ========> add -28 both side

12x + 28 -28 = 7-28

12x = -21         =======> divid both side by 12

x = -21/12 = 1.75


 

user profile pic

sbinkowski | Middle School Teacher | (Level 1) Adjunct Educator

Posted June 14, 2009 at 6:01 AM (Answer #5)

dislike 0 like

4(3x + 7) = 7

1) You can't do anything until you get rid of the parentheses. Use distributive property to get rid of those.

12x + 28 = 7

2) Now do the order of operations backwards. The first thing (going backwards) is addition/subtraction. What do you have in your problem? You have addition. The opposite of addition is subtraction.

12x + 28 = 7

-28      -28

12x          = -21

3. Now you have 12x = -21. What operation is being used in the equation? Multiplication is. The opposite of multiplication is division. Now divide both sides by 12.

12x = -21

x = -1.75

 

user profile pic

fcooper15 | Student, Grade 10 | eNotes Newbie

Posted February 18, 2010 at 11:49 AM (Answer #6)

dislike 0 like

4(3x+7)=7

4-3=1 1x7=7

user profile pic

laurto | Student, Grade 10 | Valedictorian

Posted December 8, 2013 at 1:32 AM (Answer #8)

dislike 0 like

4(3x+7)=7

you have to get rid of the parenthesis

distribute the 4 within the parentheis

12x+28=7

subtract 28 from both sides

12x+28=7

     -28    -28

12x=-21

divide by 12

12x=-21

/12    /12

x=-1.75

user profile pic

Yojana_Thapa | Student, Grade 10 | Valedictorian

Posted February 7, 2014 at 11:12 PM (Answer #9)

dislike 0 like

4(3x+7)=7

* distribute the 4

  • (4 * 3x)= 12x
  • (4 * 7) = 28

12x + 28 = 7

  • subtract 28 in both sides
  • +28 -28 = 0
  • 7 - 28 = -21

12x = -21

  • Divide 12 to both sides to get the x alone
  • (12x / 12 ) = x
  • (-21/12) = -1.75

x = -1.75

user profile pic

nicole8923 | Student, Grade 10 | Salutatorian

Posted February 26, 2014 at 7:43 PM (Answer #11)

dislike 0 like

4(3x+7)=7

12x+28=7

12x+28-28=7-28

12x=-21

12x/12=-21/12

x=-1.75

user profile pic

Wiggin42 | Student, Grade 11 | Valedictorian

Posted March 23, 2014 at 4:00 PM (Answer #12)

dislike 0 like

4(3x+7)=7

Divide both sides by 4

3x + 7 = 7/4

subtract 7

3x = (7/4) - 7

divide by 3

((7/4) - 7)/3

= -1.75

user profile pic

atyourservice | Student, Grade 10 | Valedictorian

Posted April 16, 2014 at 3:37 AM (Answer #13)

dislike 0 like

4(3x+7)=7

multiply the numbers in the parentheses (3x + 7) by the number on the outside of the parenthesis (4) 
 
`3x xx 4= 12x `
 
 
`4 xx 7 = 28 `
 
 
`12x + 28 = 7 `
 
minus 28 to combine like terms and get x alone
 
12x=-21
 
divide by 12 to get x alone
 
 
`(12x) / 12 = -21 / 12 `
 
x = -1.75
user profile pic

acompanioninthetardis | Student, Undergraduate | Valedictorian

Posted May 17, 2014 at 4:19 AM (Answer #14)

dislike 0 like

Solve for x:

4(3x+7)=7

okay so in order to do this, we stick with the golden rule: to get the unkown variable on one side of the equal side (also do the same thing to both sides) and all the other number on the other side

in order to get X by itself, you have to first divide both sides by 4

so you have (3X+7)=7/4 = 1.75

then you subtract 7 from both sides

3X= 7/4 -7 = 1.75 - 7

then divide the entire thing by 3

x= (7/4 - 7)/3 = (1.75-7)/3= (-5.25)/3= -1.75

user profile pic

parama9000 | Student, Grade 11 | Valedictorian

Posted May 31, 2014 at 3:34 PM (Answer #15)

dislike 0 like

First divide 4 on both sides.

Next, minus 7 from both sides

7/4-7=-5.25

Then divide -5.25 by 3, to get-1.75.

user profile pic

zumba96 | Student, Grade 11 | Valedictorian

Posted May 31, 2014 at 6:04 PM (Answer #16)

dislike 0 like

Since you are solving for x you need to separate the variable from the others. To do that you need to distribute the x first of all

4(3x+7)=7

12x+28=7 then move the numbers on one side and isolate the variable

12x=-21

Divide by 12

x=-21/12 = -1.75 ` <br> `

user profile pic

nisarg | Student, Kindergarten | Valedictorian

Posted June 18, 2014 at 3:51 AM (Answer #17)

dislike 0 like

4(3x+7)=7

12x+28=7    multiply by 4

12x= -21        subtract 28 from all sides

x= -21/12         divide both sides by 12

user profile pic

jess1999 | Student, Grade 9 | Valedictorian

Posted June 19, 2014 at 1:32 AM (Answer #18)

dislike 0 like

4(3x+7) = 7

Distribute the 4 : 12x + 28 = 7

subtract the 28  : 12x = -21

divide the 12     : -21 / 12

              x = -21/12 but it can be simplified

divide both sides by 3

         X = -7/4 , -1.75 , or -1 3/4

user profile pic

udonbutterfly | Student, College Freshman | Valedictorian

Posted July 30, 2014 at 2:25 PM (Answer #19)

dislike 0 like

4(3x+7)=7

First Multiply 4 by everything in the parentheses and you will get

4 X (3x) + 4 X (7) = 7

12x + 28 = 7

Now subtract 28 from both sides

(12x + 28) -28 = (7) -28 The 28 will be cancelled out on the left side.

12x = -21

Now divide -21 by 12

12(12x) = (-21)12

You should get

x = -1.75

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes